More than 500 decisions by the leading federal agency that referees disputes between labor and management will have to be reopened after the Supreme Court ruled Thursday that the five-member board had operated illegally when its membership dwindled to two.

“If Congress had intended to authorize two members alone to act for the Board on an ongoing basis, it could have said so in straightforward language,” Justice Stevens said. “Congress instead imposed the requirement that the Board delegate authority to no fewer than three members, and that it have three participating members to constitute a quorum.”

Allowing two members to run the agency because Congress and the White House can’t agree on new members would be letting the board “create a tail that would not only wag the dog, but would continue to wag after the dog has died,” Justice Stevens said.

The decision means that more than 500 of employee-employer cases decided by the NLRB while its membership had dropped to two must now be reopened by the board, which currently has four members.

“Now hundreds of decisions in cases already decided by the NLRB will have to be reopened, needlessly delaying finality for workers who were led to believe they already had it,” said Kimberly Freeman Brown, executive director of American Rights at Work.

Justice Stevens wrote the court’s opinion, and was joined by Chief Justice John G. Roberts Jr. and Justices Antonin Scalia, Clarence Thomas and Samuel A. Alito Jr.

The NLRB is an independent federal agency created by Congress in 1935 to administer the National Labor Relations Act, the primary law governing relations between unions and employers. The five members are nominated to five-year terms by the president and must be confirmed by the Senate.

But it has operated with only two members for more than two years because Democrats refused to confirm President George W. Bush’s nominees because of complaints that they were pro-business. Republicans then blocked President Obama’s nominees, complaining that some of them favor union interests.

Before the board dwindled to two members, the three-member board delegated the entire group’s authority to the chairwoman, Democrat Wilma Liebman, and Republican board member Peter Schaumber, who made more than 500 decisions.

“Nothing in the statute suggests that a delegation to a three-member group expires when one member’s seat becomes vacant,” Justice Anthony Kennedy wrote in the dissent.